Grandes déviations et applications

Ects : 6
Compétence à acquérir :
Large deviations are at the center of modern probability and statistics.
The theory originated form the risk analysis for insurance companies.
Today there are applications in almost all domains of applied mathematics.

Description du contenu de l'enseignement :
- Generalities on large deviations: Cramer Theorem and Varadhan’s lemma. Variational principles.
- Local large deviations, applications in statistical mechanics (equivalence of ensembles).
- Connection with the viscous solutions in Hamilton-Jacobi equatio